Mandela, 95, the anti-apartheid leader and first black president of South Africa, remains in critical condition and at times "unstable," Zuma said in the statement.
His doctors are "convinced that he will receive the same level of intensive care at his Houghton home that he received in Pretoria," Zuma said. "His home has been reconfigured to allow him to receive intensive care there. The health care personnel providing care at his home are the very same who provided care to him in hospital. If there are health conditions that warrant another admission to hospital in future, this will be done."
Mandela had been in the hospital since June for a lung infection.
"We thank all the health professionals at the hospital for their dedication. Most media have also been notably responsible and we thank them also for the maturity and understanding that all have in general displayed," Zuma said.
On Saturday, false news reports that Mandela had been discharged stunned the country and threw the international media into a frenzy, with a small army of media outlets scrambling to his home.
However, the reports turned out to be a false alarm and prompted Zuma to issue a statement Saturday, denying the media reports and assuring the public that Mandela was still hospitalized and was responding well to treatment.
A Mandela relative had apparently misunderstood her communication with one of Mandela's doctors and erroneously believed he had been released.
The relative informed other family members, who, in turn, relayed the faulty information to the media.
Mandela: Father of Modern South Africa
Mandela, who turned 95 in July, remains an almost mythical figure in South Africa.
After his anti-apartheid efforts landed him in jail for 27 years, he was released in February 1990 and four years later was elected the country's first black president and the first one elected by a full, non-racial democracy after the demise of apartheid.
He is widely considered the father of modern South Africa and one of the towering political figures of the 20th century.
ABC News' Rob Nelson contributed to this report.